Trigonometric Equations and Solutions

The video tutorial explains how to solve trigonometric equations using the unit circle and reference triangles. It covers solving two equations: 2cos(Theta) = sqrt(2) and 2cos(Theta) = -sqrt(3) over the interval from 0 to 2pi. The tutorial demonstrates solving these equations without a calculator by identifying the relevant quadrants and using reference triangles to find solutions. The video emphasizes understanding both methods to solve trigonometric equations effectively.

What is the main method used to solve the trigonometric equations in this lesson?

• Algebraic manipulation

• Graphical method

• Using a calculator

• Unit circle and reference triangles

In which quadrants is the cosine function positive?

• Third and fourth

• First and second

• Second and third

• First and fourth

What is the simplified form of √2/2?

• 1/√2

• √2

• 1/2

• 2/√2

Which reference triangle is used to solve the first equation?

• 60-60-60 triangle

• 45-45-90 triangle

• 30-60-90 triangle

• 30-30-120 triangle

What is the cosine value for the angle π/4?

• 1/√2

• 1

• √3/2

• 1/2

In which quadrants is the cosine function negative?

• First and second

• Second and third

• First and fourth

• Third and fourth

What is the x-coordinate for the angle 5π/6 on the unit circle?

• 1/2

• -√3/2

• √3/2

• -1/2

Which reference triangle is used to solve the second equation?

• 30-60-90 triangle

• 45-45-90 triangle

• 30-30-120 triangle

• 60-60-60 triangle

What is the cosine value for the angle π/6?

• 1

• 1/√2

• √3/2

• 1/2

What is the angle in radians for 30° in the unit circle?

• π/6

• π/2

• π/3

• π/4